Corners, Tables, Lines

The modern concept of race is usually traced back to proponents of a “natural history of mankind” in the European Enlightenment. Starting from allegorical representations of the four continents in the late sixteenth and seventeenth centuries and the eighteenth-century visual genre of castas paintings, I suggest that modern conceptions of race were significantly shaped by diagrammatic representations of human diversity that allowed for tabulation of data, combinatorial analysis, and quantification, and hence functioned as “tools to think with.” Accounting for racial ancestry in terms of “proportions of blood” not only became a preoccupation of scholars as a consequence, but also came to underwrite administrative practices and popular discourses. To contribute to a better understanding of the history of race relations, historians of the race concept need to pay more attention to these diagrammatic aspects of the concept.

Gluing idioms back together: A phraseo-combinatorial analysis

The formal analysis of idioms has been oscillating between approaches that emphasize the unit-like character of idioms and approaches that focus on the autonomy of the idioms' parts. In this paper, we summarize the main arguments for and against these two positions to then propose an account that tries to capture and combine the insights and advantages of both types of analysis. The resulting theory is heavily influenced by the approach taken in Riehemann (2001).

Stability and Bifurcations of Equilibria in Networks with Piecewise Linear Interactions

In this paper, we study equilibria of differential equation models for networks. When interactions between nodes are taken to be piecewise constant, an efficient combinatorial analysis can be used to characterize the equilibria. When the piecewise constant functions are replaced with piecewise linear functions, the equilibria are preserved as long as the piecewise linear functions are sufficiently steep. Therefore the combinatorial analysis can be leveraged to understand a broader class of interactions. To better understand how broad this class is, we explicitly characterize how steep the piecewise linear functions must be for the correspondence between equilibria to hold. To do so, we analyze the steady state and Hopf bifurcations which cause a change in the number or stability of equilibria as slopes are decreased. Additionally, we show how to choose a subset of parameters so that the correspondence between equilibria holds for the smallest possible slopes when the remaining parameters are fixed.

Combinatorial Analysis of Phenotypic and Clinical Risk Factors Associated With Hospitalized COVID-19 Patients

Characterization of the risk factors associated with variability in the clinical outcomes of COVID-19 is important. Our previous study using genomic data identified a potential role of calcium and lipid homeostasis in severe COVID-19. This study aimed to identify similar combinations of features (disease signatures) associated with severe disease in a separate patient population with purely clinical and phenotypic data. The PrecisionLife combinatorial analytics platform was used to analyze features derived from de-identified health records in the UnitedHealth Group COVID-19 Data Suite. The platform identified and analyzed 836 disease signatures in two cohorts associated with an increased risk of COVID-19 hospitalization. Cohort 1 was formed of cases hospitalized with COVID-19 and a set of controls who developed mild symptoms. Cohort 2 included Cohort 1 individuals for whom additional laboratory test data was available. We found several disease signatures where lower levels of lipids were found co-occurring with lower levels of serum calcium and leukocytes. Many of the low lipid signatures were independent of statin use and 50% of cases with hypocalcemia signatures were reported with vitamin D deficiency. These signatures may be attributed to similar mechanisms linking calcium and lipid signaling where changes in cellular lipid levels during inflammation and infection affect calcium signaling in host cells. This study and our previous genomics analysis demonstrate that combinatorial analysis can identify disease signatures associated with the risk of developing severe COVID-19 separately from genomic or clinical data in different populations. Both studies suggest associations between calcium and lipid signaling in severe COVID-19.

Forecast of cattle leukemia virus epizootic development in West Kazakhstan region

Bovine leukemia is a chronic viral infectious disease that is widespread in many countries of the world, including the Republic of Kazakhstan. Based on our spectral and combinatorial analysis, this paper presents the results of supposed scenarios of leukemia infection development in the territory of West Kazakhstan region, where there is the alternating change of ups and downs virus level having a direct dependence on solar activity. To solve this problem, we used previously developed computer programs to decompose the dynamics of the cattle infection rate in the West Kazakhstan region for 2006-2016 into a Fourier series, then generate all possible combinations, create a database table with forecast values for several years and select the best numerical series. As a result of this research, it was noted that the computer mathematical model simulating the dynamics of bovine leukemia virus (BLV) carrier, based on the properties of the trigonometric Fourier polynomial, has 100% coincidence with the actual trend. Then in order to identify trends that would maximally reflect the real trend, we conducted a combinatorial analysis of the spectral model which allowed us to increase the number of alternative scenarios for the development of BLV infection for the next five years (2021-2026). According to the above mentioned mathematical model, based on combinatorial analysis, in 2022 the forecast of infectability corridor will average from 4.15 to 11.01%; in 2023 from 3.89 to 9.76%; in 2024 from 8.04 to 16.47%; in 2025 from 6.86 to 15.23% and in 2026 from 3.98 to 8.79%.

On the automorphism group of minimal -adic subshifts of finite alphabet rank

It has been recently proved that the automorphism group of a minimal subshift with non-superlinear word complexity is virtually $\mathbb {Z}$ [Cyr and Kra. The automorphism group of a shift of linear growth: beyond transitivity. Forum Math. Sigma3 (2015), e5; Donoso et al. On automorphism groups of low complexity subshifts. Ergod. Th. & Dynam. Sys.36(1) (2016), 64–95]. In this article we extend this result to a broader class proving that the automorphism group of a minimal $\mathcal {S}$ -adic subshift of finite alphabet rank is virtually $\mathbb {Z}$ . The proof is based on a fine combinatorial analysis of the asymptotic classes in this type of subshifts, which we prove are a finite number.